The control of flexible systems has been an active area of research for many years because of its importance to a wide range of applications. The majority of previous research on time-optimal control has concentrated on the rest-to-rest problem. However, there are many cases when flexible systems are not at rest or are subjected to disturbances. This paper presents an approach to design optimal vibration-reducing commands for systems with nonzero initial conditions. The problem is first formulated as an optimal control problem, and the optimal solution is shown to be bang-bang. Once the structure of the optimal command is known, a parametric problem formulation is presented for the computation of the switching times. Solutions are experimentally verified using a portable bridge crane by moving the payload through a commanded motion while removing initial payload swing.

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